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arXiv · 2409.04444

A Note on the Carath\'{e}odory Number of the Joint Numerical Range

Beatrice Maier·Tim Netzer
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Abstract

We show that the Carath\'{e}odory number of the joint numerical range of $d$ many bounded self-adjoint operators is at most $d-1$, and even at most $d-2$ if the underlying Hilbert space has dimension at least $3$. This extension of the classical convexity results for numerical ranges shows that also joint numerical ranges are significantly less non-convex than general sets.

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Beatrice Maier, Tim Netzer. 2024-08-19. A Note on the Carath\'{e}odory Number of the Joint Numerical Range. https://arxiv.org/abs/2409.04444

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